A141125 Hankel transform of a transform of Fibonacci numbers.

1, 4, -4, -16, 16, 64, -64, -256, 256, 1024, -1024, -4096, 4096, 16384, -16384, -65536, 65536, 262144, -262144, -1048576, 1048576, 4194304, -4194304, -16777216, 16777216, 67108864, -67108864, -268435456, 268435456, 1073741824, -1073741824, -4294967296, 4294967296

Offset

0,2

Comments

Hankel transform of A100095(n+1).

Links

Table of n, a(n) for n=0..32.

Index entries for linear recurrences with constant coefficients, signature (0,-4).

Formula

G.f.: (1+4x)/(1+4x^2).

a(n) = 2^n*(cos(Pi*n/2)+2*sin(Pi*n/2)).

a(n+3) = a(n+2)*a(n+1)/a(n). - Reinhard Zumkeller, Mar 04 2011

E.g.f.: cos(2*x) + 2*sin(2*x). - Stefano Spezia, Jul 18 2025

Mathematica

LinearRecurrence[{0, -4}, {1, 4}, 33] (* James C. McMahon, Jul 17 2025 *)
(* Alternative: *)
CoefficientList[Series[(1+4x)/(1+4x^2), {x, 0, 32}], x] (* James C. McMahon, Jul 17 2025 *)

Crossrefs

Cf. A100095, A141124.

Sequence in context: A231839 A056450 A164906 * A164111 A213173 A222956

Adjacent sequences: A141122 A141123 A141124 * A141126 A141127 A141128

Keyword

easy,sign

Author

Paul Barry, Jun 05 2008

Extensions

More terms from James C. McMahon, Jul 18 2025

Status

approved